Problem 21 - Beginning and Intermediate Algebra

Question

Find each sum. $$ 6+(-6) $$

Step-by-Step Solution

Answer

0

Step 1: Identify the Numbers

Look at the numbers given in the expression. They are 6 and -6.

Step 2: Understand the Addition of Opposites

When adding a number and its negative (opposite), the result is always 0. This is because moving positive 6 units and then moving negative 6 units will bring you back to the starting point.

Step 3: Perform the Addition

Add 6 and -6 together: - 6 + (-6) = 0.

Step 4: Verify the Result

Double-check the calculation. Adding a positive number and its exact negative always equals 0.

Key Concepts

opposites in addition

When we talk about opposites in addition, we refer to a pair of numbers that are equal in magnitude but have opposite signs. For example, in the problem given, 6 and -6 are opposites. Adding these two together results in zero because they effectively cancel each other out. This happens because moving 6 units in the positive direction and then 6 units in the negative direction brings you right back to where you started.
Think of it like walking forward 6 steps and then walking backward 6 steps. You end up where you started, which is why the sum is zero.

zero property

The Zero Property of Addition states that the sum of any number and zero is the original number itself. However, there is another interesting facet of zero in addition, which we see in this exercise.
The Zero Property is highlighted when adding a number and its opposite. For example, adding 6 and -6 equals 0. You can see this as a way of balancing both positive and negative movements, leaving you at zero.
In general, whenever you're adding two exact opposites, your result will be zero due to the Zero Property!

integer operations

Understanding integer operations is crucial in solving problems with both positive and negative numbers like the one in the exercise. Integers include positive numbers, negative numbers, and zero. Here are some key points:

• Adding Positive and Negative Numbers: When you add integers with different signs, you're essentially combining their directions. Like in our exercise, 6 (positive) and -6 (negative).
• Adding Two Positive or Two Negative Numbers: When the signs are the same, you simply add their absolute values, and the result keeps that common sign. For instance, 3 + 4 = 7 and -3 + (-4) = -7.
• Subtraction as Addition: Subtraction can be thought of as adding the opposite. For example, 6 - 6 can be written as 6 + (-6).

Mastering integer operations allows you to navigate more complex problems with confidence.